Basic properties
Modulus: | \(3971\) | |
Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{209}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3971.ba
\(\chi_{3971}(28,\cdot)\) \(\chi_{3971}(62,\cdot)\) \(\chi_{3971}(415,\cdot)\) \(\chi_{3971}(750,\cdot)\) \(\chi_{3971}(776,\cdot)\) \(\chi_{3971}(821,\cdot)\) \(\chi_{3971}(1317,\cdot)\) \(\chi_{3971}(1328,\cdot)\) \(\chi_{3971}(1498,\cdot)\) \(\chi_{3971}(1678,\cdot)\) \(\chi_{3971}(1689,\cdot)\) \(\chi_{3971}(1833,\cdot)\) \(\chi_{3971}(1867,\cdot)\) \(\chi_{3971}(2228,\cdot)\) \(\chi_{3971}(2400,\cdot)\) \(\chi_{3971}(2411,\cdot)\) \(\chi_{3971}(2581,\cdot)\) \(\chi_{3971}(2626,\cdot)\) \(\chi_{3971}(2950,\cdot)\) \(\chi_{3971}(2987,\cdot)\) \(\chi_{3971}(3483,\cdot)\) \(\chi_{3971}(3494,\cdot)\) \(\chi_{3971}(3638,\cdot)\) \(\chi_{3971}(3709,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1806,2168)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{4}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 3971 }(28, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) |